{"id":6468,"date":"2017-02-19T17:10:00","date_gmt":"2017-02-19T17:10:00","guid":{"rendered":"https:\/\/theteacherstudio.com\/2017\/02\/fraction-concepts-day-2-conceptions.html"},"modified":"2026-01-19T20:01:57","modified_gmt":"2026-01-19T20:01:57","slug":"fraction-concepts-day-2-conceptions","status":"publish","type":"post","link":"https:\/\/theteacherstudio.com\/fraction-concepts-day-2-conceptions\/","title":{"rendered":"Fraction Misconceptions and Math Language (Day 2 Fraction Concepts)"},"content":{"rendered":"
Fractions can be tricky\u2014not because students aren\u2019t capable, but because misconceptions about fractions are incredibly common. In this Day 2 lesson from my Fraction Concepts series, the goal is to intentionally surface those misconceptions while helping students develop clear, accurate fraction language<\/strong>. By creating space for discussion, questioning, and mathematical talk, students start to refine their thinking and build a stronger foundation for understanding fractions in meaningful ways.<\/div>\n
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Indeed, things got even more interesting as my work with fractions unfolded on day 2! \u00a0For those of you who read my first fraction post, I discussed how we used paper folding to get our fraction concepts unit “launched”, and we ran out of time to finish the investigation before digging into some fraction misconceptions. \u00a0I gave them another 25 minutes today to work on folding their different fractional amounts and then asked them to spend some time writing in their math notebook on any of the following:<\/p>\n<\/div>\n

What did you notice?<\/div>\n
<\/div>\n
Was there anything challenging?<\/div>\n
<\/div>\n
What was easy?<\/div>\n
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 <\/p>\n

What patterns did you discover?
\n<\/a><\/div>\n

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First I gave the students “alone” time to write and then let them go compare notes with their partner from the investigation…<\/p>\n

After the students had their work time, we had a discussion about the things that they noticed…I jotted down their ideas on the Smartboard…<\/div>\n
<\/div>\n
\n
\"Recording<\/a><\/div>\n

<\/h3>\n

Math vocabulary and language<\/h3>\n

 <\/p>\n

What really stood out to me was the very NEBULOUS (vocabulary word!) math language I was hearing. \u00a0A phrase that kept coming up was “small fractions” as in “It was harder to fold the small fractions.”<\/div>\n<\/div>\n
\n
<\/div>\n<\/div>\n
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So, being the pesky and annoying teacher that I am, I presented this question to the class:<\/div>\n
<\/div>\n<\/div>\n
\"uncovering<\/a>
I L-O-V-E to ask questions like this!<\/figcaption><\/figure>\n

 <\/p>\n

So, I didn’t let the students talk . . . I just said that I was hearing MANY students use this phrase, so I thought we had better make sure we all knew what it meant. \u00a0I asked each student to write the So, answer to that question on a post it note and come slap it on the easel.<\/div>\n
\"More<\/a>
Being the obedient students that they are, they did.<\/figcaption><\/figure>\n

 <\/p>\n

And–seriously–I only wish I had taken some photos of the notes up close. \u00a0SERIOUSLY! \u00a0I had everything from . . .<\/div>\n
<\/div>\n
64<\/em><\/strong><\/div>\n
<\/div>\n
to<\/em><\/strong><\/div>\n
<\/div>\n
1\/100th<\/em><\/strong><\/div>\n
<\/div>\n
to<\/em><\/strong><\/div>\n
<\/div>\n
“When you make it smaller”<\/em><\/strong><\/div>\n
<\/div>\n
to<\/em><\/strong><\/div>\n
<\/div>\n
“Small fractions are like tenths”<\/em><\/strong><\/div>\n

 <\/p>\n

<\/div>\n
\n
At this point, any concerns I had about backing up this far and moving this slowly were GONE! \u00a0I read off the notes to the students and then asked what we had learned about what a “small” fraction is and one of my delightful yet very shy students called out, “ABsolutely nothing!” and we all laughed hysterically.<\/div>\n

 <\/p>\n<\/div>\n

What next?<\/h3>\n
\n
So where do we go from here? \u00a0I reminded the students about how we have been talking about the Common Core and how important it is to use precise mathematical language. \u00a0I asked if “small fraction” was precise enough that anyone else would know what we meant. . . and we had complete agreement that it was not.\u00a0 Next, I asked them if, on our 4, 3, 2 , 1 rubric we were evaluate how clearly we communicated, we agreed that all our post its were 1’s with a few 2’s sprinkled in . . . until “T” asked, “If there really isn’t an answer, how could someone get a 4 on this?”<\/div>\n

 <\/p>\n

<\/div>\n
Have I mentioned how much I love fourth graders? \u00a0He honestly asked–and honestly wanted to know! \u00a0I told him I had to think about it. . . always a good strategy for the tricky questions! \u00a0Don’t answer too soon!<\/div>\n

 <\/p>\n

Deep fractional thinking<\/h3>\n<\/div>\n
\n
So I set the students to work on a little activity to set them up for tomorrow’s lesson…I asked them to work completely alone to answer the following question:<\/div>\n<\/div>\n
\n
\n
\"My<\/a>
If it is too small to read, the question asks “Is this shape divided into fourths? \u00a0Explain your thinking.”<\/figcaption><\/figure>\n<\/div>\n<\/div>\n
<\/div>\n
I let them work for a few minutes and then on their way out to recess made them commit to either a “yes” or a “no” response . . . and it will be our kickoff “debate” tomorrow! \u00a0Remember, one key element of the Standards for Mathematical Practice is the ability to explain one’s own work and to critique the reasoning of others . . . so tune in tomorrow to see how it all shakes out!<\/div>\n

 <\/p>\n

<\/div>\n
After they worked for a few minutes we gathered back together to talk about T’s question . . . is it possible to get a 4 on a question with no answer? \u00a0 Maybe I should save that for another blog post . . . this one is already plenty long–but I told him that yes, I do believe you can get a 4 on a question with no answer. \u00a0I reminded him that we are stressing explaining our thinking, and we could certainly do that with this question. \u00a0I modeled something sort of like this (this was done aloud, not in writing . . . I’m just trying to give you the gist of it)<\/div>\n

 <\/p>\n

<\/div>\n
“I know that there are different ways to look at the idea of being small. \u00a0Some people might think the numbers should be small–like in 1\/2. \u00a0Some people might look at the size of the pieces to determine what a “small” fraction is. \u00a0Still others might think a small fraction is one where you only look at one piece of a whole–like 1\/3 is small where 2\/3 is big. \u00a0So for the question “What is a small fraction?”, it is very important to understand that there might be more than one way to answer it.”<\/div>\n

 <\/p>\n

Reasonable and rigorous expectations<\/h3>\n
\n

\"teaching<\/a>Would I expect a fourth grader to be able to answer like this? \u00a0Maybe not today . . . but now that it has been modeled–perhaps. \u00a0We must push their thinking, push their comfort level, and push them into the rigor that is required.<\/p>\n

If we make it meaningful, they can do it! \u00a0Thanks for sticking with me again–sorry these are getting so long! \u00a0Stay tuned to see how our debate works out . . . I’ll give you a hint–the vote was 9 “yes” to 13 “no”!<\/p>\n<\/div>\n

 <\/p>\n

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 <\/p>\n<\/div>\n

***UPDATE***<\/div>\n
This blog post is now a part of my comprehensive fraction unit available by clicking the image below. \u00a0Hundreds of teachers have now used it to change the way they teach fractions!<\/div>\n
\"3rd<\/a><\/div>\n
Now available as a part of a ten-resource fraction toolbox that might help you teach to deep understanding.<\/div>\n

\"Fraction<\/a><\/p>\n

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Did you miss\u00a0Day 1<\/a>\u00a0 of this fraction series?\u00a0 Go take a look!<\/strong><\/div>\n

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Hey there!\u00a0 Looking for more?\u00a0<\/strong><\/em><\/div>\n
Follow me on social media and by email!<\/strong><\/em><\/div>\n
<\/div>\n
You can find me on\u00a0Facebook<\/a>,\u00a0Tiktok<\/a>,\u00a0Instagram<\/a>, and\u00a0Pinterest<\/a>\u00a0and<\/div>\n
you can also\u00a0sign up for my NEWSLETTER<\/a>\u00a0where I start you off with an awesome freebie\u2013and then you will get even more teaching tips, freebies, and offers delivered right to your mailbox!<\/div>\n
\"\"<\/div>\n<\/div>\n<\/div>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Fractions can be tricky\u2014not because students aren\u2019t capable, but because misconceptions about fractions are incredibly common. In this Day 2 lesson from my Fraction Concepts series, the goal is to intentionally surface those misconceptions while helping students develop clear, accurate fraction language. By creating space for discussion, questioning, and mathematical talk, students start to refine […]<\/p>\n","protected":false},"author":2,"featured_media":11941753,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2,343],"tags":[225,194,179,224,182,178,186],"class_list":["post-6468","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-lessons","category-fractions","tag-common-core","tag-fractions","tag-math","tag-mathematical-practice","tag-problem-solving","tag-reading","tag-writing","wpbf-post"],"acf":[],"yoast_head":"\nFraction Misconceptions and Math Language (Day 2 Fraction Concepts) - The Teacher Studio<\/title>\n<meta name=\"description\" content=\"Helping students find fraction misconceptions is an essential part of what we need to do. 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